Calculating concentrations
The concentrationA measure of the mass or amount of solute dissolved in a given volume of solvent or solution. of a solutionMixture formed by a solute and a solvent. can be measured in g dm-3 or in mol dm-3. It is more useful to know the concentration of a reactantA substance that reacts together with another substance to form products during a chemical reaction. in mol dm-3 as the amountIn chemistry, a measure of the number of particles in a substance. of reactant in a given volume can be calculated.
Concentration using moles
The concentration of a solution can be calculated using:
- the amount of dissolvedA substance is said to be dissolved when it breaks up and mixes completely with a solvent to produce a solution.soluteThe dissolved substance in a solution. in moleThe amount of substance that contains the same number of particles as there are atoms in 12 g of carbon-12 (contains the Avogadro's constant 6.0 脳10虏鲁 number of particles). (mol)
- the volume of solution (or solventThe liquid in which the solute dissolves to form a solution.) in cubic decimetres (dm3)
The units for concentration can also be shown as mol dm3 or M (for 'molar'), but these mean the same as mol dm3.
Worked example
0.5 mol of sodium hydroxide is dissolved in 2 dm3 of water. Calculate the concentration of the sodium hydroxide solution formed.
Concentration in mol dm-3 = \(\frac{\textup{amount~of~solute~in~mol}}{\textup{volume~in~dm}^3}\)
Concentration = \(\frac{\textup{0.5~mol}}{\textup{2~dm}^3}\)
Concentration = 0.25 mol dm-3
Volume units
Volumes used in concentration calculations must be in dm3, not in cm3. It is useful to know that 1 dm3 = 1,000 cm3. This means:
- divide by 1,000 to convert from cm3 to dm3
- multiply by 1,000 to convert from dm3 to cm3
For example, 250 cm3 is 0.25 dm3 (250 梅 1000). It is often easiest to convert from cm3 to dm3 before continuing with a concentration calculation.
Question
100 cm3 of dilute hydrochloric acid contains 0.02 mol of dissolved hydrogen chloride. Calculate the concentration of the acid in mol dm-3.
Volume of acid = 100 梅 1000 = 0.1 dm3
concentration of acid = 0.02 梅 0.1
= 0.2 mol dm-3
Converting between units
The relative formula massThe sum of the relative atomic masses of the atoms in a chemical formula., Mr, of the solute is used to convert between mol dm-3 and g dm-3:
- to convert from mol dm-3 to g dm-3, multiply by the Mr
- to convert from g dm-3 to mol dm-3, divide by the Mr
Worked example
Calculate the concentration of 0.1 mol dm-3 sodium hydroxide solution in g dm-3. (Mr of NaOH = 40)
Concentration = 0.1 脳 40
= 4 g dm-3